Let (xybe the value of the linear functionalyεE*on the elementxεE, whereEis a Banach space with conjugateE*Tbe a unit circumference of a complex plane; and Σ be a a σ-algebra of Borel subsets ofT. Let a functionh:T→E*be strongly measurable and for ∀xεEa functionbe summable. An explicit proof is given that if a set function μσ →>E*, ∀xεE, is a vector measure with a finite total variation, then the function h is Bochner integrable.